jmc

We must find the radius of the circle in order to find the area. We are told that points $A$ and $B$ are the endpoints of a diameter, so we use the distance formula to find the length of the diameter.

$$\begin{array}{rl}\sqrt{(-1-3{)}^2+(-2-2{)}^2}& =\sqrt{16+16}\\ & =4\sqrt{2}\end{array}$$Since the diameter has a length of $4\sqrt{2}$, the radius must have length $2\sqrt{2}$. Therefore, the answer is $(2\sqrt{2}{)}^2\pi =\boxed{8\pi }$.